Progress in FY2007 was made in the following areas: [unreadable] [unreadable] (1) STOCHASTIC DIPOLAR RECOUPLING IN SOLID STATE NMR: An entirely new approach to measurements of interatomic distances in molecular solids that are uniformly 13C-labeled (or contain many active nuclei of other types) was developed theoretically and implemented experimentally. This new approach is called "stochastic dipolar recoupling", because it is a form of dipolar recoupling that involves stochastic parameters. Dipolar recoupling means a radiofrequency pulse sequence that is applied in synchrony with magic-angle sample spinning (MAS) in order to switch on nuclear magnetic dipole-dipole couplings, which depend on interatomic distances as 1/R3. The stochastic parameters are randomly-chosen offsets of radiofrequency carrier frequencies during free-evolution periods that separate dipolar recoupling periods. The effect of stochastic dipolar recoupling is to convert the fixed dipole-dipole couplings that are usually used to measure interatomic distances in solid state NMR to randomly fluctuating couplings, which produce well-defined rates of interatomic nuclear spin polarization transfers that are strictly proportional to 1/R6. Under stochastic dipolar recoupling, nuclear spin polarization transfer data (normally recorded in two-dimensional solid state NMR spectra) can be analyzed with simple kinetics, described by an N X N rate matrix for an N-spin system. In contrast, similar data obtained with traditional techniques do not follow simple kinetic equations (because of quantum mechanical interferences between non-commuting pairwise dipole-dipole couplings), and can only be analyzed by diagonalization of 2N X 2N Hamiltonian matrices (which is impossible for large spin systems). Preliminary experiments demonstrating stochastic dipolar recoupling were performed on simple two-spin and five-spin 13C-labeled compounds. This work is described in a manuscript that will soon be published in Physical Review Letters. Additional theoretical aspects of stochastic dipolar recoupling (including derivation of a simple analytical expression for polarization transfers in two-spin systems that covers the entire progression from coherent to incoherent evolution) are described in a manuscript that is currently under review for the Journal of Physical Chemistry. [unreadable] [unreadable] The idea for stochastic dipolar recoupling is an outgrowth of frequency-selective dipolar recoupling methods that our group has developed and continues to refine. Frequency-selective dipolar recoupling was first described by us in a paper in J. Chem. Phys., vol. 124, p. 194303, year 2006. [unreadable] [unreadable] (2) ULTRA-LOW-TEMPERATURE SOLID STATE NMR: Nearly all solid state NMR studies of interesting systems are limited by signal detection sensitivity. The sensitivity (i.e., signal-to-noise ratio) of solid state NMR measurements increases with decreasing sample temperature, approximately as 1/T1.5. Therefore, in principle, measurements at 30 K have thirty-fold higher sensitivity than measurements at room temperature, meaning that the time to complete a measurement can be reduced by a factor of 30 X 30 = 900 by operating at 30 K (since signal-to-noise is proportional to the square root of measurement time) if sample size is fixed. Alternatively, sample size requirements can be reduced by a factor of thirty. For these reasons, it is important to develop new solid state NMR technology for ultra-low-temperature measurements. To this end, we have constructed a prototype solid state NMR probe (which means the device that contains the sample and radiofrequency circuitry within the magnet of an NMR spectrometer) that can be cooled to 30 K by helium vapor. The probe has full capabilities for magic-angle spinning, triple-resonance operation, and high-power radiofrequency pulse sequences. No such probe is available from commercial sources, and no such probe has been demonstrated previously by other research groups. Our tests to date indicate that magic-angle spinning frequencies up to 7 kHz, temperatures down to 35 K, and radiofrequency fields up to 100 kHz can be achieved, with sample volumes of approximately 100 microliters. Liquid helium consumption is currently 4 liters per hour, but we expect this to be reduced when thermal insulation is improved. Experiments with various paramagnetic relaxation enhancement agents indicate that a dysprosium-EDTA complex can reduce proton spin-lattice relaxation times in frozen solutions to approximately 5 seconds at 35 K. Given these parameters, we anticipate that successful experiments on real protein samples will be carried out in early FY2008. Major initial applications of this ultra-low-temperature technology will be in structural studies of freeze-trapped unfolded states of proteins and in studies of beta-amyloid oligomers that are transient intermediates in amyloid formation.[unreadable] [unreadable] (3) SYMMETRY-BASED CONSTANT-TIME DIPOLAR RECOUPLING: As described above, dipolar recoupling techniques are methods for measuring nuclear magnetic dipole-dipole couplings, and hence interatomic distances, in solid state NMR. Since these couplings depend on distances as 1/R3, intermolecular couplings (at distances greater than 4 angstroms) are quite weak, being less than 70 Hz at 5 angstroms for 13C pairs. As demonstrated in previous work in our group, accurate measurements of long-distance couplings require "constant-time" dipolar recoupling techniques, meaning radiofrequency pulse sequences that have a constant total duration and constant number of pulses, while the effective dipolar recoupling time is varied by rearrangements of pulses within the pulse sequence. In FY2007, we have developed and demonstrated a new type of constant-time dipolar recoupling that is particularly simple and experimentally robust, based on symmetry principles of recoupling sequences under time translation. This work is described in J. Chem. Phys., vol 126, p. 064506, year 2007. We now use symmetry-based constant-time dipolar recoupling in measurements of intermolecular distances that define beta-sheet structure in amyloid fibrils, and in measurements of inter-residue 15N-15N distances that constrain the conformations of peptide backbones at specific sites within amyloid fibrils.